If A + C = B, then tan A,tan B,tan C =

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3.Trigonometrical Ratios, Functions and Identities

easy

If $A + C = B,$ then $\tan A\,\tan B\,\tan C = $

A

$\tan A\,\tan B + \tan \,C$

B

$\tan \,B - \tan \,C - \tan \,A$

C

$\tan A + \tan C - \tan B$

D

$ - \,(\tan A\tan B + \tan C)$

Solution

(b) $B = A + C \Rightarrow \tan B = \tan (A + C)$

==> $\tan B = \frac{{\tan A + \tan C}}{{1 – \tan A\tan C}}$

==> $\tan A\tan B\tan C = \tan B – \tan A – \tan C$.

Standard 11

Mathematics

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